The terahertz band has been recognized as a promising candidate to support future rate-greedy applications such as 6G communications. Optoelectronic terahertz communications are beneficial for the realization of high-speed transmission. In this Letter, we propose and experimentally demonstrate an optoelectronic terahertz transmission system with intensity modulation and direct detection, where a discrete multitone (DMT) waveform with high-order quadrature amplitude modulation (QAM) is used. A zero-bias diode (ZBD) is used in the system as a simple, cost-effective direct detection terahertz receiver. A nonlinearity-aware digital signal reception routine is proposed to mitigate the nonlinear impairments induced by subcarrier-to-subcarrier beating interference from the ZBD. In this experiment, up to a 60 Gbit/s line rate 16QAM-DMT signal is successfully transmitted over a 3 m wireless link in the 310 GHz band, and the mean signal-to-noise ratio is improved by 3 dB with nonlinearity-aware signal processing routine. The advantageous features of such a scheme make it a promising solution for terahertz wireless communications.